Local solvability, blow-up, and Hölder regularity of solutions to some Cauchy problems for nonlinear plasma wave equations: II. Potential theory

Volume and surface potentials arising in Cauchy problems for nonlinear equations in the theory of ion acoustic and drift waves in a plasma are considered, and their properties are examined. For the volume potential, an estimate is derived, which is used to prove a Schauder-type a priori estimate and Schauder-type estimates for weighted potentials.